##### 4.10.3 $$(-y(x)-2 x+5) y'(x)-2 y(x)-x+4=0$$

ODE
$(-y(x)-2 x+5) y'(x)-2 y(x)-x+4=0$ ODE Classiﬁcation

[[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]]

Book solution method
Equation linear in the variables, $$y'(x)=f\left ( \frac {X_1}{X_2} \right )$$

Mathematica
cpu = 0.164567 (sec), leaf count = 53

$\left \{\left \{y(x)\to -\sqrt {3 x^2-12 x+25+c_1}-2 x+5\right \},\left \{y(x)\to \sqrt {3 x^2-12 x+25+c_1}-2 x+5\right \}\right \}$

Maple
cpu = 0.184 (sec), leaf count = 32

$\left [y \left (x \right ) = 1-\frac {2 \textit {\_C1} \left (x -2\right )+\sqrt {3 \left (x -2\right )^{2} \textit {\_C1}^{2}+1}}{\textit {\_C1}}\right ]$ Mathematica raw input

DSolve[4 - x - 2*y[x] + (5 - 2*x - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> 5 - 2*x - Sqrt[25 - 12*x + 3*x^2 + C[1]]}, {y[x] -> 5 - 2*x + Sqrt[25
- 12*x + 3*x^2 + C[1]]}}

Maple raw input

dsolve((5-2*x-y(x))*diff(y(x),x)+4-x-2*y(x) = 0, y(x))

Maple raw output

[y(x) = 1-(2*_C1*(x-2)+(3*(x-2)^2*_C1^2+1)^(1/2))/_C1]